Vibration control system

ABSTRACT

A vibration control device, while applying Gaussian vibration that matches a target vibration physical quantity PSD to a test piece, makes a corresponding vibration physical quantity non-Gaussian. Using a response vibration physical quantity PSD and a target vibration physical quantity PSD, a control vibration physical quantity PSD calculation generates a control vibration physical quantity PSD for generating a drive signal. A PSD conversion converts the control vibration physical quantity PSD into a control corresponding vibration physical quantity PSD of another dimension. Using the control corresponding vibration physical quantity PSD, a control corresponding vibration physical quantity waveform calculation calculates a control corresponding vibration physical quantity waveform that is non-Gaussian. At least based on the control characteristics and the control corresponding vibration physical quantity waveform, a drive waveform calculation generates a next drive waveform such that vibration that matches the control corresponding vibration physical quantity waveform is applied to a test piece.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a national stage application under 35 U.S.C. 371 ofPCT Application No. PCT/JP2019/041305 having an international filingdate of 21 Oct. 2019, which designated the United States, which PCTapplication claimed the benefit of Japanese Application No. 2019-015493,filed 31 Jan. 2019, each of which are incorporated herein by referencein their entirety.

TECHNICAL FIELD

One exemplary aspect of the present invention relates to a vibrationcontrol system for controlling vibration generated by a vibrationgenerator in a vibration tester that is used to simulate a vibrationenvironment.

BACKGROUND ART

A random vibration test is a method for experimentally verifying thatperformance, reliability, and durability of a test object satisfies adesired design by subjecting the test object to a prescribed vibrationenvironment and checking a state of the test object during the vibrationtest or after the test. In general, a goal of the test is achieved byreference acceleration PSD (power spectral density). Accelerationvibration used for excitation is requested “to be stationary Gaussianrandom vibration”.

However, the concept of Gaussian distribution (normal distribution)includes that, in principle, acceleration with an extremely large(theoretically infinite) peak occurs with an extremely low probability(being just about nil). It is impossible to create a system thatliterally reproduces the above. In addition, preparation for theextremely large peak, which hardly occurs, means a significant waste ofeffort. Thus, when the system is actually realized, a condition isrelaxed to rationally achieve the following, a “probability densityfunction (PDF) includes a signal that is at least 36 or higher accordingto the Gaussian distribution”.

In the present specification, hereinafter, the signal, for which thecondition of a request for a Gaussian property to create the systemunder such meaning is relaxed, will simply be referred to as a “Gaussiansignal” according to customary practice.

It is known that, when an acceleration signal of random vibration is theGaussian signal, corresponding vibration waveform of velocity,displacement, jerk (a rate of change of the acceleration as a temporalchange rate of the acceleration), or the like as a kinematic quantity ofanother dimension related to the same vibration also obeys to theGaussian distribution. This is considered as part of the natural lawobserved extremely widely and applied also to unbiased random vibrationsin general that is subject to the Central Limit Theorem.

For example, in regard to a system disclosed in U.S. Pat. No. 5,012,428(corresponding to Japanese Examined Patent Application PublicationJP1994-5192B (HEI6-5192B)) by the inventors of the present application,and incorporated herein by reference, a vibration control system forvibrating a test object according to an acceleration waveform with theGaussian property while satisfying reference acceleration PSD isdisclosed.

In addition, in Japanese Patent 5421971B (Japanese Laid-open PatentApplication Publication JP2013-88125A) and Japanese Patent 6518631B(Japanese Laid-open Patent Application Publication JP2018-21781A by theinventors of the present application, and incorporated herein byreference, a vibration control system for vibrating a test objectaccording to an acceleration waveform with a non-Gaussian property whilesatisfying the reference acceleration PSD is disclosed.

SUMMARY

However, it is requested to make any of the other kinematic quantitiesof the different dimensions, such as velocity, displacement, and jerk,have the “non-Gaussian property” while satisfying the request for theprescribed acceleration PSD. The techniques disclosed in above mentionedpatent documents and Japanese Patent 1961722B (Japanese Laid-open PatentApplication Publication JP1990-184906A) cannot meet such a request.

As an example, in regard to sensitivity of a human person related tosensing of a change in motion, sensitivity for the jerk is higher thansensitivity for the acceleration. Thus, in order to improve ride qualityor alleviate a harmful effect on a body, a train, an elevator, a rollercoaster, and the like, are designed to reduce a jerk amount. In such acase, in the case where the jerk amount included in a test waveform ischanged from that in the Gaussian distribution according to the design,an experiment having a vibration condition that is close to an actualcondition can be conducted as the random vibration test.

In addition, in general, the vibration tester has limitations onspecifications related to the maximum velocity, maximum displacement,and the like in addition to the maximum excitation force and maximumacceleration that can be output according to the basic specifications.In the case where the signal of the velocity or the displacement exceedsthe maximum specification thereof even for a moment while theacceleration falls within the maximum specification thereof, a safetysystem is actuated at the moment, which possibly interrupts the test. Insuch a case, as long as a maximum peak value of the velocity or thedisplacement can rationally be controlled to a certain value or lower,it is possible to reliably avoid such a situation where the vibrationexceeding a limit of such an amount occurs to stop the test regardlessof a coincidence.

In an electrodynamic vibration generator, a maximum velocity of avibrator (an armature) is restricted by the maximum voltage that can beoutput by the amplifier, and maximum displacement thereof is restrictedby a mechanical dimension that is related to a movable range of thevibrator. In the case where the maximum voltage that can be output bythe amplifier is insufficient, as long as a reference velocity waveformis clipped in advance such that a maximum peak value thereof fallswithin a limit value (in this way, the velocity waveform acquires anon-Gaussian property. In order to keep the non-Gaussian property, suchcontrol has to be executed that a response velocity waveform observed ata response point remains the same as the waveform itself) and theacceleration waveform corresponding to this vibration motion canmaintain the request for the PSD, the above problem can be solved whilethe goal of the test is satisfied.

Similarly, in the case where displacement limitation is problematic, aslong as a Gaussian acceleration random signal with the acceleration PSDrequested for the test is achieved at a response point and acorresponding displacement signal can be reproduced as a non-Gaussianrandom signal, a peak value of which reliably falls within a certainvalue, the vibration test can be conducted without a possibility ofdiscontinuation of the test caused by excess of the displacementlimitation.

Here, similar to the above, it is requested to make the drive signalhave the “non-Gaussian property” while satisfying the request for PSD ofthe prescribed kinematic quantity.

In addition, it is generally requested to vibrate the test object thatis placed on the vibration generator with vibration having a desiredwaveform. As disclosed in Japanese Patent 1961722B (Japanese Laid-openPatent Application Publication JP1990-184906A), the inventors of thepresent application have already invented a system that meets such arequest. However, in this system, the vibration of the test object isdetected by an acceleration sensor. Thus, the vibration can only becontrolled such that the acceleration waveform of the vibration matchesto a reference acceleration waveform that is determined in advance.

In regard to a physical quantity of the other dimension such as avelocity waveform, the vibration of the test object can be controlled byproviding a velocity sensor or the like and applying the referencewaveform of the desired vibration. However, the provisioning of manytypes of sensors is complicated and thus is not preferred.

For this reason, such a vibration control system is desired that canexecute acceleration PSD control by using an acceleration sensor (or asensor for the other dimension) while executing waveform control of thekinematic quantity having a different dimension from acceleration.

It is one object of the present invention to provide a vibration controlsystem capable of solving any of the above problems and creating variousadditional values upon the conducting of a test.

In the present specification, with respect to a vibration physicalquantity of a certain dimension, a vibration physical quantity ofanother different dimension indicating behaviors of the same vibrationwill be referred to as a corresponding physical quantity. Some aspectsof the present invention each of which can be applied independently aredescribed as follows:

(1) (2) A vibration control system according to the present inventioncomprises: a vibration physical quantity detection sensor which detectsa vibration physical quantity of a test object that is vibrated by avibration generator operated at least based on a drive waveform; meansfor calculating a response vibration physical quantity PSD by subjectinga response vibration physical quantity waveform from the vibrationphysical quantity detection sensor to the Fourier transform; means forcalculating corresponding vibration physical quantity PSD for control ofa different dimension, which corresponds to the vibration physicalquantity PSD for control, at least based on the response vibrationphysical quantity PSD and reference vibration physical quantity PSD;means for calculating a non-Gaussian random waveform of thecorresponding vibration physical quantity for control by subjectingspectrum data, which is generated from the corresponding vibrationphysical quantity PSD for control, to the inverse Fourier transform inorder to obtain the desired non-Gaussian characteristics in thetime-domain, and setting the non-Gaussian random waveform of thecorresponding vibration physical quantity for control as a correspondingvibration physical quantity waveform for control; means for calculatingthe drive waveform at least based on the corresponding vibrationphysical quantity waveform for control with inverse characteristics oftransfer characteristics of a system including a vibration generator andthe test object as the equalization object; and means for modifying theequalization characteristics at least based on the drive waveform andthe response vibration

Accordingly, it can be achieved to carry out the control where thecorresponding vibration physical quantity has non-Gaussiancharacteristics, while the test object is vibrated according to thereference vibration physical quantity PSD with non-Gaussiancharacteristics.

(3) In the vibration control system according to the present invention,the means for calculating corresponding vibration physical quantity PSDfor control includes: means for calculating vibration physical quantityPSD for control by comparing the response vibration physical quantityPSD and the reference vibration physical quantity PSD such that theresponse vibration physical quantity PSD matches to the referencevibration physical quantity PSD; and means for converting the vibrationphysical quantity PSD for control into the corresponding vibrationphysical quantity PSD for control of the different dimension.

Accordingly, corresponding vibration physical quantity PSD for controlcan be generated such that reference vibration physical quantity PSDmatches to response vibration physical quantity PSD.

(4) In the vibration control system according to the present invention,the means for calculating corresponding vibration physical quantity PSDfor control includes: means for converting the response vibrationphysical quantity PSD into response corresponding vibration physicalquantity PSD of the different dimension; means for converting thereference vibration physical quantity PSD into reference correspondingvibration physical quantity PSD of the different dimension; and meansfor modifying the corresponding vibration physical quantity PSD forcontrol by comparing the response corresponding vibration physicalquantity PSD and the reference corresponding vibration physical quantityPSD such that the response corresponding vibration physical quantity PSDmatches to the reference corresponding vibration physical quantity PSD.

Accordingly, corresponding vibration physical quantity PSD for controlcan be generated such that reference vibration physical quantity PSDmatches response vibration physical quantity PSD.

(5) In the vibration control system according to the present invention,the means for calculating corresponding vibration physical quantitywaveform for control includes: means for acquiring a Gaussian randomwaveform of the corresponding vibration physical quantity for control bysubjecting amplitude spectrum data, which is generated from thecorresponding vibration physical quantity PSD for control, to theinverse Fourier transform with providing uniformly distributed randomphases; means for converting the Gaussian random waveform of thecorresponding vibration physical quantity for control into thenon-Gaussian random waveform at least based on non-Gaussian conversioncharacteristics; means for extracting the phase information of frequencycomponents of a non-Gaussian signal phases by subjecting thenon-Gaussian random waveform to the Fourier transform; and means forcalculating the non-Gaussian random waveform of the correspondingvibration physical quantity for control by subjecting the correspondingvibration physical quantity PSD for control to the inverse Fouriertransform by providing the non-Gaussian signal phases.

Accordingly, the test object can be vibrated according to thecorresponding vibration physical quantity waveform for control bycarrying out the control based on response vibration physical quantityand drive waveform.

(6) In the vibration control system according to the present invention,the means for calculating corresponding vibration physical quantitywaveform for control includes: means for obtaining Gaussian randomwaveform of a corresponding vibration physical quantity for control bysubjecting amplitude spectrum data, which is generated from thecorresponding vibration physical quantity PSD for control, to theinverse Fourier transform with providing uniformly distributed randomphases; and means for converting the Gaussian random waveform of thecorresponding vibration physical quantity for control into thenon-Gaussian random waveform at least based on non-Gaussian conversioncharacteristics such that the non-Gaussian random waveform of thecorresponding vibration physical quantity for control is obtained.

Accordingly, the test object can be vibrated according to correspondingvibration physical quantity waveform for control by carrying out thecontrol based on response vibration physical quantity and drivewaveform.

(7) In the vibration control system according to the present invention,the non-Gaussian conversion characteristic is a ZMNL (Zero-MemoryNon-Linear) function.

(8) In the vibration control system according to the present invention,the feature of the non-Gaussian conversion characteristics is to limit apeak value such that the Gaussian random waveform of the correspondingvibration physical quantity for control does not exceed a prescribedlimit value, and in the case where the Gaussian random waveform of thecorresponding vibration physical quantity for control does not exceedthe limit value, said Gaussian random waveform of the correspondingvibration physical quantity for control is used as the non-Gaussianrandom waveform of the corresponding vibration physical quantity forcontrol.

Accordingly, control can be achieved such that the correspondingvibration physical quantity waveform for control fits within limit.

(9) In the vibration control system according to the present invention,the means for calculating a drive waveform performs convolutionoperation on the corresponding vibration physical quantity waveform forcontrol by using an impulse response as the equalizationcharacteristics, so as to calculate the drive waveform, and the meansfor modifying equalization characteristics calculates the equalizationcharacteristics as a reciprocal of a value obtained by dividing thecorresponding vibration physical quantity with the vibration physicalquantity transfer function, at least based on a spectrum of a responsecorresponding vibration physical quantity waveform, which is convertedfrom the response vibration physical quantity waveform, and a spectrumof the drive waveform.

Accordingly, while the response waveform is detected by a vibrationphysical quantity, the test object can be vibrated according to thewaveform of corresponding vibration physical quantity of differentdimension

(10) In the vibration control system according to the present invention,the means for modifying equalization characteristics includes: means forcalculating the vibration physical quantity transfer function at leastbased on the drive waveform and the response vibration physical quantitywaveform; means for converting the vibration physical quantity transferfunction into the corresponding vibration physical quantity transferfunction; and means for calculating the equalization characteristics asa reciprocal of the corresponding vibration physical quantity transferfunction.

Accordingly, while the response waveform is detected by a vibrationphysical quantity, the test object can be vibrated according to thewaveform of corresponding vibration physical quantity of differentdimension.

(11) In the vibration control system according to the present invention,the means for calculating drive waveform includes: means for convertingthe corresponding vibration physical quantity waveform for control intoa non-Gaussian random waveform of the vibration physical quantity forcontrol; and control means for performing the convolution operation onthe physical vibration quantity waveform for control by using theimpulse response of the reciprocal of the system including the vibrationgenerator and the test object as the equalization characteristics, so asto calculate the drive waveform.

Accordingly, while the response waveform is detected by a vibrationphysical quantity, the test object can be vibrated according to thewaveform of corresponding vibration physical quantity of differentdimension

(12) In the vibration control system according to the present invention,the vibration physical quantity detection sensor is a sensor thatdetects any of displacement, velocity, acceleration, and jerk ofvibration, and the vibration physical quantity is any of thedisplacement, the velocity, the acceleration, and the jerk.

Accordingly, the control can be carried out at any dimension concerningdisplacement, velocity, acceleration, and jerk of vibration.

(13) (14) A vibration control system in accordance with the presentinvention comprises: an acceleration sensor for detecting accelerationof a test object that is vibrated by a vibration generator operated atleast based on a drive waveform; means for acquiring responseacceleration PSD by subjecting a response acceleration waveform from theacceleration sensor to the Fourier transform; means for calculatingvibration physical quantity PSD for control corresponding toacceleration PSD for control at least based on the response accelerationPSD and reference acceleration PSD, the vibration physical quantity PSDfor control being displacement PSD for control, velocity PSD forcontrol, or jerk PSD for control; means for obtaining Gaussian randomwaveform of a corresponding vibration physical quantity for control bysubjecting amplitude spectrum data, which is generated from thedisplacement PSD for control, the velocity PSD for control, or the jerkPSD for control, to the inverse Fourier transform with providinguniformly distributed random phases, Gaussian random waveform of acorresponding vibration physical quantity for control being a Gaussianrandom waveform of the displacement for control, a Gaussian randomwaveform of the velocity for control, or a Gaussian random waveform ofthe jerk for control; determination means for providing drive waveformcalculation means with the Gaussian random waveform of the displacementfor control, the Gaussian random waveform of the velocity for control,or the Gaussian random waveform of the jerk for control as is as adisplacement waveform for control, a velocity waveform for control, or ajerk waveform for control in the case where a portion that exceeds alimit value is not present in said Gaussian random waveform of thedisplacement for control, or said Gaussian random waveform of thevelocity for control, or said Gaussian random waveform of the jerk forcontrol in a prescribed unit period, and providing the drive waveformcalculation means with a non-Gaussian random waveform of thedisplacement for control, a non-Gaussian random waveform of the velocityfor control, or a non-Gaussian random waveform of the jerk for control,which is calculated by non-Gaussian conversion means, non-Gaussiansignal phase extraction means, or waveform calculation means, as thedisplacement waveform for control, the velocity waveform for control, orthe jerk waveform for control in the case where the portion that exceedsthe limit value is present; means for calculating the drive waveform atleast based on the displacement waveform for control, the velocitywaveform for control, or the jerk waveform for control with inversecharacteristics of a transfer function of a system including a vibrationgenerator and the test object as equalization characteristics; means forcalculating an acceleration transfer function at least based on thedrive waveform and the response acceleration waveform; means forconverting the acceleration transfer function into a displacementtransfer function, a velocity transfer function, or a jerk transferfunction; and inverse transfer function calculation means forcalculating the equalization characteristics as a reciprocal of thedisplacement transfer function, the velocity transfer function, or thejerk transfer function.

Accordingly, it can be achieved to carry out the control where thecorresponding vibration physical quantity has non-Gaussiancharacteristics, while the test object is vibrated according to thereference vibration physical quantity PSD with non-Gaussiancharacteristics.

(15) (17) A vibration control system for vibrating a test object in amanner to match a reference vibration physical quantity waveform of asecond dimension that differs from a first dimension of a drive waveformfor vibrating the test object and of a response vibration physicalquantity waveform, with which vibration of the test object is detectedin accordance with the present invention comprises: a vibration physicalquantity detection sensor which detects a vibration physical quantity ofthe test object that is vibrated by a vibration generator operated atleast based on the drive waveform, so as to output the responsevibration physical quantity waveform; means for calculating the drivewaveform at least based on the reference vibration physical quantitywaveform by using an equalization characteristics as inversecharacteristics of transfer characteristics of a system including avibration generator and the test object; and means for modifying theequalization characteristics as a reciprocal of a second dimensiontransfer function at least based on the response vibration physicalquantity waveform and the drive waveform, the second dimension transferfunction being a ratio between a spectrum of the drive waveform and aspectrum of a second response vibration physical quantity waveform,which is generated by converting the response vibration physicalquantity waveform into that of the second dimension.

Accordingly, while the response waveform is detected by the vibrationphysical quantity, the test object can be vibrated according to thewaveform of corresponding vibration physical quantity of differentdimension.

(16) (18) A vibration control system according to the present inventioncomprises: means for acquiring response vibration physical quantity PSDby subjecting a response vibration physical quantity waveform from thevibration physical quantity detection sensor to Fourier transform; meansfor calculating vibration physical quantity PSD for control at leastbased on the response vibration physical quantity PSD and the referencevibration physical quantity PSD such that the response vibrationphysical quantity PSD matches the reference vibration physical quantityPSD; and means for calculating vibration physical quantity waveform forcontrol by subjecting spectrum data, which is generated from thevibration physical quantity PSD for control, to the inverse Fouriertransform, and providing the vibration physical quantity waveform forcontrol as the reference vibration physical quantity waveform to thedrive waveform calculating means.

Accordingly, the test object can be vibrated where the control iscarried out in order to match the response vibration physical quantitywith the reference vibration physical quantity PSD and the responsewaveform matches with the reference waveform of corresponding vibrationphysical quantity of different dimension.

(19) In the vibration control system according to the present invention,the equalization characteristics modification means includes: means forcalculating a first dimension transfer function at least based on thedrive waveform and the response vibration physical quantity waveform;means for converting the first dimension transfer function into thesecond dimension transfer function; and inverse transfer functioncalculation means for calculating the equalization characteristics as areciprocal of the second dimension transfer function.

Accordingly, while the response waveform is detected by the vibrationphysical quantity of first dimension, the test object can be vibratedaccording to the waveform of corresponding vibration physical quantityof different second dimension.

(20) In the vibration control system according to the present invention,the equalization characteristics modification means includes: responsevibration physical quantity waveform conversion means for converting theresponse vibration physical quantity waveform into a second responsevibration physical quantity waveform; means for calculating the seconddimension transfer function at least based on the drive waveform and thesecond response vibration physical quantity waveform; and inversetransfer function calculation means for calculating the equalizationcharacteristics as the reciprocal of the second dimension transferfunction.

Accordingly, while the response waveform is detected by the vibrationphysical quantity of first dimension, the test object can be vibratedaccording to the waveform of corresponding vibration physical quantityof different second dimension.

(21) (22) A vibration control system according to the present inventioncomprises: a vibration physical quantity detection sensor which detectsa vibration physical quantity of a test object that is vibrated by avibration generator operated at least based on a drive waveform; meansfor acquiring response vibration physical quantity PSD by subjecting aresponse vibration physical quantity waveform from the vibrationphysical quantity detection sensor to the Fourier transform; means forcontrolling drive PSD at least based on the response vibration physicalquantity PSD, reference vibration physical quantity PSD, the responsevibration physical quantity waveform, and the drive waveform; and meansfor calculating a non-Gaussian random drive waveform by subjectingspectrum data, which is generated from the drive PSD, to the inverseFourier transform, and setting the non-Gaussian random drive waveform asthe drive waveform in order to obtain desired non-Gaussiancharacteristics.

Accordingly, the test object can be vibrated according to the referencevibration physical quantity PSD where the drive waveform is madenon-Gaussian characteristics.

-   -   “means for calculating a response vibration physical quantity        PSD” at least corresponds to step S2 in the embodiment.    -   “means for calculating vibration physical quantity PSD for        control” at least corresponds to step S3 in the embodiment.    -   “means for calculating vibration physical quantity PSD for        control” at least corresponds to step S3 in the embodiment.    -   “means for converting PSD” at least corresponds to step S4 in        the embodiment.    -   “means for calculating Gaussian waveform of corresponding        vibration physical quantity for control” at least corresponds to        step S5 in the embodiment.    -   “means for converting Gaussian waveform into non-Gaussian        waveform” at least corresponds to step S6 in the embodiment.    -   “means for extracting phase” at least corresponds to step S7 in        the embodiment.    -   “means for converting to non-Gaussian” at least corresponds to        step S8 in the embodiment.    -   “means for calculating drive waveform” at least corresponds to        steps S11-S14 or steps S51-S54 in the embodiment.    -   “means for calculating transfer function” at least corresponds        to step S17 or S57 in the embodiment.    -   “means for converting transfer function” at least corresponds to        step S18 or S58 in the embodiment.    -   “means for calculating inverse-transfer function” at least        corresponds to step S19 or S59 in the embodiment.    -   “program” is a concept that includes not only a program that can        directly be executed by a CPU, processor or controller, but also        a program and/or instructions in a source format, a program        subjected to compression processing, an encrypted program,        and/or the like.

Any one or more of the functions/means described herein and/or inassociation with the accompanying figures/flowcharts, can be encoded asinstructions, stored in the memory and executed by the CPU/processor.The instructions can also be part of a control program running on anoperating system (OS) with any one or more of the inputs,determinations, calculations and/or outputs capable of being displayedon the display and/or output to the vibration generator. Applicant hasexpressed these functions/means in an understandable format thatincludes one or more of mathematical formula, in prose, and/or in a flowchart(s), and thus have provided sufficient structure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a functional block diagram of a vibration control systemaccording to an embodiment of the present invention.

FIG. 2 illustrates a hardware configuration of the vibration controlsystem.

FIG. 3 is a flowchart of a vibration control program.

FIG. 4 is a flowchart of the vibration control program.

FIG. 5A illustrates an example of reference acceleration PSD, FIG. 5Billustrates an example of response acceleration PSD, FIG. 5C illustratesan example of acceleration PSD for control, and FIG. 5D illustrates anexample of modified acceleration PSD for control.

FIG. 6A illustrates velocity PSD for control and original accelerationPSD for control, FIG. 6B illustrates a Gaussian random waveform ofvelocity for control and a forcibly clipped waveform, and FIG. 6C is agraph illustrating the Gaussian random waveform of velocity for controland a softly clipped waveform.

FIG. 7A illustrates an example of a window function, and FIG. 7B to FIG.7F are views for illustrating an overlap procedure of windowedwaveforms.

FIG. 8A illustrates an example of a reference acceleration waveform, andFIG. 8B illustrates an example of a reference velocity waveform, a peakof which is limited.

FIG. 8C illustrates an example of an amplitude probability densityfunction (PDF), for which the reference acceleration waveform and thereference velocity waveform are subjected to a histogram analysis, and atheoretical PDF of Gaussian distribution, and FIG. 8D illustrates anexample of a drive waveform.

FIG. 8E illustrates an example of a response acceleration waveform, andFIG. 8F illustrates an example of a response velocity waveform.

FIG. 8G illustrates an example of a PDF as a result of the histogramanalysis of the response acceleration waveform and the response velocitywaveform, and FIG. 8H illustrates an example of the responseacceleration PSD (a solid line), the reference acceleration PSD (adotted line), and drive voltage PSD (a one-dot chain line).

FIG. 9 is a view illustrating another example of corresponding physicalquantity PSD for control calculation means 30.

FIG. 10 is a view illustrating another example of drive waveformcalculation means 50 and equalization characteristics modification means60.

FIG. 11 is a view illustrating another example of corresponding physicalquantity waveform for control calculation means 40.

FIG. 12 illustrates an example of a ZMNL function.

FIG. 13 is a view illustrating a relationship between two each ofdimensions of a physical quantity describing motion.

FIG. 14 is a functional block diagram of a vibration control systemaccording to a second embodiment.

FIG. 15 is a flowchart of the vibration control program.

FIG. 16 is a view illustrating another example of equalizationcharacteristics modification means 60.

FIG. 17 is a functional block diagram of a vibration control systemaccording to another example.

FIG. 18 is a functional block diagram of a vibration control systemaccording to yet another example.

DESCRIPTION OF EMBODIMENTS 1. First Embodiment

1.1 Functional Configuration

FIG. 1 is a functional configuration diagram of a vibration controlsystem according to an embodiment of the present invention. In thisembodiment, an amplifier 80, a vibration generator 2, a test object 4,and a vibration physical quantity detection sensor 6 are provided forcontrol/evaluation by the vibration control system.

The test object 4 as a test target is placed on the vibration generator2. The vibration physical quantity detection sensor 6 detects vibrationof the test object 4 that is vibrated by the vibration generator 2. Adisplacement sensor, a velocity sensor, an acceleration sensor, a jerksensor, or the like can be used as the vibration physical quantitydetection sensor 6. A signal representing a response vibration physicalquantity (a displacement signal, a velocity signal, an accelerationsignal, a jerk signal, or the like) from the vibration physical quantitydetection sensor 6 is converted into a response vibration physicalquantity waveform (hereinafter referred as response physical quantitywaveform) as digital data by an A/D converter 10. The response physicalquantity waveform is data in which characteristics of the vibration isexpressed by a dimension such as displacement, a velocity, acceleration,or jerk.

Response vibration physical quantity PSD calculation means 20(hereinafter referred as response physical quantity PSD calculationmeans 20) performs the Fast Fourier Transform (FFT) on the responsephysical quantity waveform to calculate response vibration physicalquantity PSD (hereinafter referred as response physical quantity PSD)thereof. Means 30 for calculating corresponding vibration physicalquantity PSD for control (hereinafter referred as means 30 forcalculating corresponding physical quantity PSD for control) calculatesa corresponding vibration physical quantity PSD for control (hereinafterreferred as corresponding physical quantity PSD for control) at leastbased on the response physical quantity PSD and reference vibrationphysical quantity PSD (hereinafter referred as reference physicalquantity PSD).

In the present specification, with respect to a vibration physicalquantity of a certain dimension, a vibration physical quantity ofanother different dimension indicating behaviors of the same vibrationwill be referred to as a corresponding physical quantity. Thus, thedimension of the above-described response physical quantity PSD differsfrom the dimension of the corresponding physical quantity PSD forcontrol.

In this embodiment, the means 30 for calculating corresponding physicalquantity PSD for control includes means 32 for calculating vibrationphysical quantity PSD for control (hereinafter referred as means 32 forcalculating quantity PSD for control) and PSD conversion means 34. Themeans 32 for calculating control physical quantity PSD calculatesvibration physical quantity PSD for control (hereinafter referred asphysical quantity PSD for control) such that the response physicalquantity PSD matches the reference physical quantity PSD. This isbecause, even when the vibration with the reference physical quantityPSD is applied to the vibration generator 2, the vibration of the testobject 4 differs from the vibration indicated by the reference physicalquantity PSD due to appropriateness or inappropriateness betweenpresence of transfer characteristics of a system including the testobject 4 and control resolution at the time of setting a non-linearfluctuation of the system or setting a control system. Thus, thephysical quantity PSD for control is successively modified andcalculated such that the response physical quantity PSD matches thereference physical quantity PSD.

The PSD conversion means 34 converts the thus-calculated physicalquantity PSD for control into the corresponding physical quantity PSDfor control of the different dimension. Thus, in this embodiment,control is executed by using the corresponding physical quantity of thedifferent dimension from the dimension, the vibration physical quantityof which is detected.

Means 40 for calculating corresponding vibration physical quantitywaveform for control (hereinafter referred as means 40 for calculatingcorresponding physical quantity waveform for control) calculates acorresponding vibration physical quantity waveform for control(hereinafter referred as corresponding physical quantity waveform forcontrol) so as to achieve a desired non-Gaussian characteristics atleast based on the corresponding physical quantity PSD for control.

In this embodiment, the means 40 for calculating corresponding physicalquantity waveform for control includes means 42 for calculating Gaussiancorresponding vibration physical quantity waveform for control,non-Gaussian conversion means 44, phase extraction means 46, andwaveform calculation means 48.

The means 42 for Gaussian corresponding physical quantity waveform forcontrol calculates a Gaussian random waveform of the correspondingphysical quantity for control by providing the corresponding physicalquantity PSD for control with uniformly distributed random phases. Thenon-Gaussian conversion means 44 calculates a non-Gaussian randomwaveform by processing the Gaussian random waveform of the correspondingphysical quantity for control at least based on prescribed non-Gaussiancharacteristics. For example, the non-Gaussian conversion means 44converts an amplitude of a corresponding physical quantity waveform forcontrol by using a ZMNL function or the like, and performs an operation(clipping) to limit the amplitude of the corresponding physical quantitywaveform for control such that the amplitude (an absolute value) doesnot exceed a prescribed value.

The phase extraction means 46 calculates frequency characteristics ofphase components of this non-Gaussian random waveform. The waveformcalculation means 48 calculates a non-Gaussian random waveform of thecorresponding physical quantity for control at least based on thecorresponding physical quantity PSD for control and phases thereof, andsets this as the corresponding physical quantity waveform for control.

Accordingly, as long as the test object 4 can be vibrated as indicatedby this corresponding physical quantity waveform for control, it ispossible to apply the vibration, the corresponding physical quantity ofwhich is made to be non-Gaussian, to the test object 4 while satisfyingthe reference physical quantity PSD.

Drive waveform calculation means 50 modifies the corresponding physicalquantity waveform for control to calculate a drive waveform at leastbased on an equalization characteristics, for which a transfer functionof the system is considered.

Equalization characteristics modification means 60 successively updatesthe above equalization characteristics at least based on the responsephysical quantity waveform and the drive waveform.

In this embodiment, the equalization characteristics modification means60 includes transfer function calculation means 62, transfer functionconversion means 64, and inverse transfer function calculation means 66.The transfer function calculation means 62 calculates a vibrationphysical quantity transfer function (hereinafter referred as physicalquantity transfer function) at least based on the response physicalquantity waveform and the drive waveform. The transfer functionconversion means 64 converts the physical quantity transfer functioninto a corresponding physical quantity transfer function. The inversetransfer function calculation means 66 inverts the correspondingphysical quantity transfer function to calculate a correspondingvibration physical quantity inverse transfer function (hereinafterreferred as corresponding physical quantity inverse transfer function).

The corresponding physical quantity inverse transfer function as theequalization characteristics, which is modified as described above, isused to calculate the drive waveform in the drive waveform calculationmeans 50.

The calculated drive waveform is converted into a drive signal by a D/Aconverter 70, is amplified by the amplifier 80, and is provided to thevibration generator 2.

1.2 Hardware Configuration

A description will hereinafter be made on a case where a randomvibration test is performed under conditions that the acceleration PSDmatches reference acceleration PSD, that the velocity that matches to orhigher than a limit value, and the like. It is requested to control thevelocity in a manner not to exceed the limit value in the case wherethere is a limitation on an output voltage of the amplifier 80.

FIG. 2 illustrates a hardware configuration of the vibration controlsystem. The vibration generator 2 has a vibration table (notillustrated) on which the test object 4 is placed and fixed. Thevibration generator 2 vibrates this vibration table. In order to detectthis vibration, the test object 4 is provided with an accelerationsensor 6 as the vibration physical quantity detection sensor(hereinafter referred as physical quantity detection sensor).

In this embodiment, the acceleration sensor 6 is used to acquire theacceleration as a response vibration physical quantity (hereinafterreferred as response physical quantity). However, a displacement sensor,a velocity sensor, and/or a jerk sensor may be used to acquire, as theresponse physical quantity, displacement, velocity, and/or jerk of theother dimension.

A memory 92, a touchscreen display 94, non-volatile memory 96, the D/Aconverter 70, and the A/D converter 10 are connected to a CPU 90. Here,output to the vibration generator 2 is provided as an analog signal tothe vibration generator 2 via the D/A converter 70 and the amplifier 80.Meanwhile, input from the acceleration sensor 6 is imported as thedigital data via the A/D converter 10.

In the non-volatile memory 96, an operating system 97 and a controlprogram 98 are recorded. The control program 98 cooperates with theoperating system 97 to exert a function thereof.

1.3 Vibration Control Processing

FIG. 3 and FIG. 4 each illustrate a flowchart of the control program 98.A description will hereinafter be made on control in the case where thetest object 4 is applied with the vibration that has the referenceacceleration PSD as illustrated in FIG. 5A and is limited such that anyabsolute value of velocity amplitude does not exceed a limit value. Thelimit values of the reference acceleration PSD and the velocityamplitude are input from the touchscreen display 94 or the like by auser and are recorded in the non-volatile memory 96.

The CPU 90 imports a response acceleration waveform from theacceleration sensor 6 for a prescribed period (hereinafter referred asone frame) via the A/D converter 10 (step S1). Furthermore, the CPU 90performs the Fast Fourier Transform (FFT) on this response accelerationwaveform to calculate response acceleration PSD (step S2). FIG. 5Billustrates an example of the calculated response acceleration PSD. Inthis embodiment, the response acceleration PSD of the responseacceleration waveform for the single frame is calculated. However, theresponse acceleration PSD of the response acceleration waveform forprescribed frames in the past may be calculated.

Next, the CPU 90 compares the response acceleration PSD and thereference acceleration PSD and modifies acceleration PSD for controlsuch that the response acceleration PSD matches the referenceacceleration PSD (step S3). For example, it is assumed that theacceleration PSD for control at the time when the above responseacceleration PSD is acquired is as illustrated in FIG. 5C. That is, itis assumed that, when the vibration generator 2 is operated with thevibration that is generated at least based on this acceleration PSD forcontrol, the response acceleration PSD illustrated in FIG. 5B isacquired.

Some parts of the response acceleration PSD illustrated in FIG. 5B donot match the reference acceleration PSD. The CPU 90 compares magnitudesof unmatched parts per frequency component (referred to as a frequencyline). Per frequency component, the acceleration PSD for control isincreased when the response acceleration PSD is lower than the referenceacceleration PSD, and the acceleration PSD for control (FIG. 5C) isreduced when the response acceleration PSD is higher than the referenceacceleration PSD. The CPU 90 makes such modification and calculates thenew acceleration PSD for control as illustrated in FIG. 5D.

Next, the CPU 90 integrates the generated acceleration PSD for control,in other words, the CPU 90 converts the generated acceleration PSD forcontrol into a velocity PSD for control of the different dimension (stepS4). FIG. 6A illustrates a comparison between the velocity PSD forcontrol, which is acquired by the conversion, and the originalacceleration PSD for control. Despite the different dimensions, thevelocity PSD for control and the original acceleration PSD for controlare illustrated on the same graph screen for the comparison.

The CPU 90 determines an amplitude component of a velocity spectrum fromthis velocity PSD for control and performs the inverse Fast FourierTransform (inverse FFT) by providing the uniform random phase to each ofthe components, so as to acquire a velocity waveform for control for thesingle frame (step S5). Due to provision of the uniformly distributedrandom phases, the generated velocity waveform for control has aGaussian property.

Next, the CPU 90 clips this Gaussian random waveform of the velocity forcontrol by the limit value (step S6). FIG. 6B illustrates the Gaussianrandom waveform of the velocity for control, which is generated in stepS5, and the clipped waveform. In FIG. 6B, limit values THU and THL areillustrated. The clipped waveform, portions of which exceeding orfalling below respective one of the limit values THU, THL are flattened,is obtained.

When such a velocity waveform is obtained by forcibly clipping thevelocity waveform for control by the limit values, just as described,the following is considered. It is possible to prevent a voltage of theamplifier 80 at the time of vibrating the test object 4 from exceedingthe limit value. However, in reality, a high-frequency component, whichis not included in the original waveform and is located on the outsideof a control band, is present in the clipped portion. For this reason,it is impossible to control the waveform while maintaining such awaveform. In addition, this waveform has the PSD that does not match thevelocity PSD for control. Thus, when the velocity waveform for control,which is forcibly clipped, in FIG. 6B is used as is, the referenceacceleration PSD illustrated in FIG. 5A cannot be achieved.

In view of the above, in this embodiment, this problem is solved asfollows. The CPU 90 performs the Fast Fourier Transform of the clippedvelocity waveform illustrated in FIG. 6B to calculate frequencycharacteristics of the phase (step S7). Next, the CPU 90 provides phaseinformation of this clipped waveform to the amplitude spectrum, which isdetermined from the velocity PSD for control in FIG. 6A, performs theinverse Fast Fourier Transform (inverse FFT), so as to generate anon-Gaussian random waveform of the velocity for control for the singleframe (step S8). This non-Gaussian random waveform of the velocity forcontrol is set as the velocity waveform for control that is a referencewaveform for waveform control. In this way, a peak value of the waveformis kept within a designated limit value while the velocity PSD forcontrol is maintained.

Here, it may be determined whether the non-Gaussian random waveform ofthe velocity for control, which is generated as described above, exceedsthe limit value. If the non-Gaussian random waveform of the velocity forcontrol exceeds the limit value, the processing in steps S6 to S8 may beexecuted for the non-Gaussian random waveform of the velocity forcontrol, and may repeatedly be executed until the non-Gaussian randomwaveform of the velocity for control does not exceed the limit value. Inthe case where the non-Gaussian random waveform of the velocity forcontrol, which does not exceed the limit value, cannot be acquired evenafter the execution of the processing for prescribed times, theprocessing may return to step S5, and the Gaussian random waveform ofvelocity for control for the single frame may be generated again.

In step S6, in the case where the Gaussian random waveform of velocityfor control for the single frame does not exceed the limit value andthus does not have to be clipped, this Gaussian random waveform ofvelocity for control may be used as is as the velocity waveform forcontrol.

FIG. 6C illustrates an example of the waveform in which all points inthe single frame fall within the limit value while the velocity PSD forcontrol, which is obtained through the above-described processing, ismaintained. A mark of simple clipping is no longer present on thiswaveform, and the waveform is subjected to so-called soft clipping.

When the velocity waveform for control is acquired as described above,the CPU 90 multiplies the velocity waveform for control for a singleframe by a window function (step S9). For example, as illustrated inFIG. 7A, such a function is used that has zero value at the initial timepoint and at the terminal time point of the single frame and has amaximum value at the central time point. Such a function is preferredthat becomes unity as a total value at all the time points when each ofthe functions is shifted by certain width and superimposed on eachother.

A property that should be provided to the window function used at thistime is described in U.S. Pat. No. 5,012,428 (corresponding to JapaneseExamined Patent Application Publication JP1994-5192B) mentioned before.In addition, processing for shifting waveform data of a wave packet,which is generated by the multiplication of the window function, by 1/Mof the width of the frame and superimposing the shifted waveform data oneach other is executed. In this case, a value of M has to satisfy acertain condition that is determined by the characteristics of the usedwindow function (see U.S. Pat. No. 5,012,428). Just as described, acertain degree of freedom is available for selection of the windowfunction and the numerical value M. However, usually, the Hanning windowfunction is used, and the minimum value of M in this case is 4. In thepresent specification, the case of M=4 will be exemplified.

When the operation of shifting the velocity waveforms, each of which ismultiplied by the window function, and superimposing the velocitywaveforms on each other continues, the velocity waveform for control, inwhich the velocity waveforms for control (pseudo random waveforms)having a discrete spectrum per frame are consistently put together in acontinuous manner, is generated. Since such waveform data does not haveany definite period, the waveform is an irregular waveform (a truerandom waveform) and thus has a continuous spectrum. In addition, eachwindowed waveform is smoothly converged to zero at the initial timepoint and the terminal time point of the frame. Thus, there is nounnecessary frequency component at a connection point.

Just as described, the CPU 90 shifts the velocity waveforms for control,each of which is multiplied by the window function, by ¼ frame andsuperimposes the shifted velocity waveforms for control on each other(step S10). Thus, when the processing in steps S1 to S10 is repeated, asillustrated in FIGS. 7B to 7E, the windowed waveforms, each of which isshifted by ¼ frame, are superimposed on each other. As a result, thecontinuous velocity waveform for control as illustrated in FIG. 7F canbe acquired.

Here, it may be examined whether one frame of the continuous velocitywaveform for control contains a point that exceeds the limit value. If asingle point in the frame of the continuous velocity waveform forcontrol exceeds the limit value, the velocity waveform for control maybe recalculated again.

Next, the CPU 90 takes out the single frame from the continuous velocitywaveform for control (step S11). However, in the real-time drive signalgeneration process, which is executed per frame, the frames possiblybecome non-continuous if they are directly connected. To handle such aproblem, the following overlapping processing is executed (steps S12,S13, S14). The waveform data is taken out by shifting the initial pointby ½ frame. Then, the waveform data is multiplied by the Hanning windowto generate the waveform for equalization. Thereafter, a convolutionoperation is performed on the thus-generated waveform by using animpulse response as the equalization processing to generate a drivesignal waveform. The drive signal waveforms are sequentially shifted by½ frame, superimposed on each other, and connected to each other.

The CPU 90 performs the convolution operation on the single frame ofvelocity waveform for control, which is taken out, by using the impulseresponse as the equalization characteristics, so as to generate thedrive signal (step S13). In this embodiment, as the equalizationcharacteristics, an inverse of the transfer function of a systemincluding the vibration generator 2 and the test object 4 is used. Thatis, in order to vibrate the test object 4 with the velocity waveform forcontrol, the convolution operation is performed on the velocity waveformfor control by using the impulse response, which corresponds to theinverse characteristics of the transfer function, so as to generate thewaveform as the drive waveform. In this way, the test object 4 can bevibrated with the velocity waveform for control. However, the transferfunction may be used as the equalization characteristics.

While executing the overlapping processing for shifting the velocitywaveforms for control, each of which is multiplied by the windowfunction, by ½ frame and superimposing the velocity waveforms forcontrol, the CPU 90 connects the thus-generated drive signals (stepsS12, S14). In this way, the CPU 90 generates the continuous drivewaveform and outputs this drive waveform to the amplifier 80 via the D/Aconverter 70 (step S15).

As a result, the vibration generator 2 is provided with the drive signalthat is amplified by the amplifier 80, and thus can vibrate the testobject 4. At this time, such processing is executed to prevent thevelocity waveform for control from exceeding the limit value, thevoltage of the amplifier 80 does not exceed an allowed maximum voltage.

Next, the CPU 90 acquires the response acceleration waveform from theacceleration sensor 6 (step S16). Then, the CPU 90 calculates anacceleration transfer function of the system at least based on theacquired drive waveform and the response acceleration waveform (stepS17). That is, the response acceleration signal is subjected to the FFTto calculate a response acceleration spectrum (including phaseinformation), and the drive waveform is subjected to the FFT tocalculate a drive spectrum (including phase information). As a ratiobetween the acceleration spectrum and the drive spectrum, theacceleration transfer function is calculated from both of the responseacceleration spectrum and the drive spectrum.

Next, this acceleration transfer function is integrated and is convertedinto a velocity transfer function (step S18). That is, the accelerationtransfer function is converted into the velocity transfer function as aratio between the velocity spectrum and the drive spectrum. A reciprocalof the velocity transfer function is calculated, and is updated as theequalization characteristics (step S19). This equalizationcharacteristics is used when the drive signal is generated next time.

Meanwhile, a value that is obtained by dividing the squared responseacceleration spectrum by the frequency resolution Δf is averaged to haveprescribed statistical degree of freedom (DOF) defined by a randomvibration test condition, so as to calculate the response accelerationPSD (step S2). Then, this response acceleration PSD is compared to thereference acceleration PSD, and acceleration PSD data for control ismodified such that an error therebetween approaches zero (step S3).

The CPU 90 repeatedly executes the processing that has been described sofar. In this way, the test object 4 can be applied with the vibrationthat is the Gaussian acceleration vibration having the desiredacceleration PSD and in which the corresponding velocity waveform hasthe non-Gaussian property.

The operations, which have been described so far, are sequentiallyapplied. As a result, a non-Gaussian random vibration controller isformed. FIGS. 8A to H illustrate an example in which a new functionalityprovided to the conventional random vibration controller by thetechnique of the present invention is briefly illustrated. The exampleillustrates data in the case where all the data of the velocitywaveform, which is determined from reference velocity PSD, is measuredby using a standard deviation σ (matches an RMS value due to lack of DCcomponent), and a peak thereof is limited in a manner not to exceed avalue corresponding to ±2.7σ. FIG. 8A illustrates a referenceacceleration waveform that is generated at least based on the data onthe reference acceleration PSD in FIG. 6A by performing theabove-described operation. A level corresponding to +3σ and a levelcorresponding to −3σ are indicated by dotted lines. Since theacceleration signal is distributed to regions outside these levels.Thus, it is considered that this signal has the Gaussian property.

Meanwhile, FIG. 8B illustrates the velocity waveform, a peak of which islimited by a level corresponding to ±2.7σ of the velocity generated bythe above-described operation. It is found that the entire velocitywaveform data are distributed in the region in the inside of the dottedlines indicative of the levels of ±3σ, more specifically, within thelevel corresponding to ±2.7σ. This signal has a non-Gaussian property.

FIG. 8C is a graph in which the reference acceleration waveform and thereference velocity waveform described above are each subjected to ahistogram analysis to calculate an amplitude probability densityfunction (PDF) and is plotted with theoretical PDF of the Gaussiandistribution. It is clearly indicated that, while the PDF of thereference acceleration waveform substantially matches the PDF of theGaussian distribution, the PDF of the reference velocity waveformdeviates from the PDF of the Gaussian distribution. In particular,absence of any data point in the outside of ±2.7σ clearly indicates thatthe velocity peak value can be limited as the purpose of the presentinvention.

In the non-Gaussian random controller of the present invention,equalization processing is executed for the reference velocity waveformby the above-described method for the waveform control such that thisreference velocity waveform is not changed as a waveform, and the drivewaveform is thereby generated. FIG. 8D illustrates an example of thedata on the drive waveform. This drive waveform is output to theamplifier 80, the amplifier drives the vibration generator 2, andresultant of the drive waveform is detected as the response accelerationwaveform by the acceleration sensor that is placed on a control point 6on vibration table 4. FIG. 8E illustrates an example of the responseacceleration waveform. It is found that, since this signal isdistributed in the region in the outside of the level of ±3σ, thissignal has the Gaussian property.

Meanwhile, FIG. 8F illustrates response velocity waveform data. Theresponse velocity waveform data is calculated by using a differentialequation system that describes a dynamic process in which the drivewaveform, which is generated by equalizing the reference velocitywaveform by the method for the waveform control, passes through acontrolled system, and by integrating the differential equation. (Theresponse acceleration waveform data in FIG. 8E is also calculated inthis way). As illustrated in this drawing, it is found that the waveformcontrol is executed as desired and the entire response velocity waveformdata is distributed in the region in the inside of the dotted linesindicative of the levels of ±3σ, more specifically, within the levelcorresponding to ±2.7σ. This signal has a non-Gaussian property.

FIG. 8G is a graph in which the PDFs as a result of the histogramanalysis of these response acceleration waveform and response velocitywaveform are plotted together. It is clearly indicated that, while thePDF of the response acceleration waveform substantially matches the PDFof the Gaussian distribution, the PDF of the response velocity waveformdeviates from the PDF of the Gaussian distribution. In particular, theabsence of the data point in the outside of ±2.7σ clearly indicates thatthe waveform control is executed as desired and the velocity peak valuecan be limited as the purpose of the present invention.

Finally, FIG. 8H is a graph in which the response acceleration PSD (asolid line) is plotted with the drive voltage PSD (a one-dot chainline). The drive voltage PSD is controlled to have such characteristicsthat equalizes the characteristics of the controlled system. In thisway, the response acceleration waveform keeps the Gaussian property, andthe PSD thereof matches the reference acceleration PSD (the dotted line)well. Meanwhile, as illustrated in FIGS. 8F, 8G, the response velocitywaveform is reproduced as a random signal that has a non-Gaussianproperty and, all the data points of which fall within a region betweenthe specified limit values.

In regard to a waveform such as a sine wave, a property of which as thewaveform is defined deterministically, regardless of whether theproperty is defined by velocity or acceleration, the same physicalphenomenon (vibration) is observed as a kinematic quantity of differentdimension. Thus, it is needless to say that the vibration as an actualentity is the same. However, the random vibration that is handled hereinis not a deterministic signal but an irregular signal, the waveform ofwhich changes over time, and in which the exactly same waveform neverappears again. Thus, the random vibration has a probabilistic property.In the random vibration test, the vibration to be reproduced is definedby assuming presence of a stationary stochastic process for providingthe actual vibration environment and designating the actual vibration bythe reference acceleration PSD. That is, only an acceleration amplitudespectrum (and the Gaussian property of the acceleration waveform) isdefined. Thus, it can be said that the random vibration has a vastamount of degree of freedom in the phase quantity. What the presentinventors have achieved in the present invention is to generate such avibration that has the Gaussian property as the acceleration waveformbut has a non-Gaussian property as the velocity waveform by using thesignificant degree of freedom in the phase. As a non-Gaussian property,the peak value exceeding 2.7σ never appears, for example. Such a mattercan be achieved in the world of the irregular waveform.

1.4 Other

(1) In the above embodiment, as illustrated in FIG. 1 , the means 30 forcalculating corresponding physical quantity PSD for control includes thecontrol physical quantity PSD calculation means 32 and the PSDconversion means 34. That is, the physical quantity PSD for control iscalculated from the response physical quantity PSD and the referencephysical quantity PSD, and the corresponding physical quantity PSD forcontrol is acquired at least based on the physical quantity PSD forcontrol.

However, as illustrated in FIG. 9 , the means 30 for calculatingcorresponding physical quantity PSD for control may include conversionmeans 31, conversion means 33, and means 35 for modifying correspondingphysical quantity PSD for control. The conversion means 31 converts thereference physical quantity PSD into reference corresponding physicalquantity PSD. The conversion means 33 converts the response physicalquantity PSD into response corresponding physical quantity PSD.

The means 35 for modifying corresponding physical quantity PSD forcontrol calculates the corresponding physical quantity PSD for controlsuch that the response corresponding physical quantity PSD is equal tothe reference corresponding physical quantity PSD.

(2) In the above embodiment, as illustrated in FIG. 1 , the drivewaveform is calculated at least based on the corresponding physicalquantity waveform for control and in consideration of the equalizationcharacteristics.

However, as illustrated in FIG. 10 , waveform conversion means 51 maydifferentiate (integrate) the corresponding physical quantity waveformfor control and converts the corresponding physical quantity waveformfor control into a physical quantity waveform for control. For example,an acceleration waveform for control can be acquired by differentiatingthe velocity waveform for control.

In the control means 53, the drive waveform can be obtained at leastbased on the physical quantity waveform for control, which is obtainedby the conversion just as described, and in consideration of theequalization characteristics.

As the equalization characteristics in this case, a reciprocal of aresponse physical quantity transfer function, which is obtained at leastbased on the drive waveform and a response physical quantity waveform,is used. Thus, as illustrated in FIG. 10 , the equalizationcharacteristics modification means 60 includes the transfer functioncalculation means 62 and the inverse transfer function calculation means66.

(3) In the above embodiment, as illustrated in FIG. 1 , the means 40 forcalculating corresponding physical quantity waveform for controlincludes the means 42 for calculating Gaussian corresponding physicalquantity waveform for control, the non-Gaussian conversion means 44, thephase extraction means 46, and the waveform calculation means 48. Thatis, the phase information of the non-Gaussian corresponding physicalquantity waveform for control is extracted, and the correspondingphysical quantity waveform for control is calculated at least based onthe corresponding physical quantity PSD for control and the phaseinformation thereof. In this way, the non-Gaussian correspondingphysical quantity waveform for control can be acquired whilecorresponding physical quantity PSD for control is maintained (that is,the reference physical quantity PSD is maintained).

However, in the case where the reference physical quantity PSD does nothave to be maintained directly and accurately, as illustrated in FIG. 11, PSD control may be executed with the corresponding physical quantityPSD for control being a direct control target, and the non-Gaussianrandom waveform of the corresponding physical quantity for control,which is converted by the non-Gaussian conversion means 44, may be usedas is as the corresponding physical quantity waveform for control.

(4) In the above embodiment, as illustrated in FIG. 1 , the equalizationcharacteristics modification means 60 includes the transfer functioncalculation means 62, the transfer function conversion means 64, and theinverse transfer function calculation means 66.

However, as illustrated in FIG. 16 , the equalization characteristicsmodification means 60 may include conversion means 61, the transferfunction calculation means 62, and the inverse transfer functioncalculation means 66. The conversion means 61 converts the responsephysical quantity waveform into response corresponding physical quantitywaveform. The transfer function calculation means 62 calculates acorresponding physical quantity transfer function at least based on thedrive waveform and the response corresponding physical quantitywaveform. The inverse transfer function calculation means 66 calculatesa reciprocal of the corresponding physical quantity transfer function asthe equalization characteristics.

(5) In the above embodiment, as an example of generating a non-Gaussianproperty by the non-Gaussian conversion means 44, the description hasbeen made on the case of clipping. However, the amplitude of a Gaussianrandom waveform of the corresponding physical quantity for control maybe converted by using a ZMNL function as exemplified in FIG. 12 tocalculate a non-Gaussian random waveform.

Alternatively, some desired non-Gaussian characteristics (such asKurtosis or Skewness) may be applied to generate a non-Gaussian randomwaveform having the desired non-Gaussian characteristics.

(6) In the above embodiment, the description has been made on the casewhere the velocity waveform for control achieves a non-Gaussian property(clipped or the like). However, the above embodiment can be appliedsimilarly to a case where a displacement waveform for control achievesthe similar non-Gaussian property (clipped or the like).

For example, it is possible to conduct such a vibration test in which amaximum value of the displacement waveform for control is limited byclipping to prevent the vibration generator 2 from exceeding an allowedmaximum displacement thereof. Here, in step S4, the acceleration PSD forcontrol may be integrated twice to obtain displacement PSD for control.Then, at least based on this displacement PSD for control, thedisplacement waveform for control can be obtained.

Similarly, jerk PSD for control can be obtained by differentiating theacceleration PSD for control. Then, at least based on this jerk PSD forcontrol, a jerk waveform for control can be obtained. Accordingly, it ispossible to execute such control that clips the jerk waveform.

Furthermore, in the above description, the response accelerationwaveform is acquired as the response physical quantity. However, aresponse waveform of another dimension such as the response velocitywaveform, a response displacement waveform, or a response jerk waveform.

(7) In the above embodiment, the description has been made on the casewhere the reference acceleration PSD is provided as the reference PSD.However, the above embodiment can be applied similarly to a case wherethe physical quantity of the other dimension is provided as thereference PSD.

(8) In the above embodiment, in step S10 and step S11, the velocitywaveforms for control are respectively shifted by ¼ frame or ½ frame andare superimposed on each other. However, the velocity waveforms forcontrol may be shifted by 1/M frame and be superimposed on each other.

(9) In the above embodiment, the drive waveform is calculated at leastbased on the velocity waveform for control, the velocity transferfunction (the ratio between the spectrum of the drive waveform and thespectrum of the response velocity waveform) is calculated at least basedon the response acceleration waveform and the drive waveform, and thereciprocal thereof is set as the equalization characteristics.

The selection of the transfer function depends on the dimension, thephysical quantity of which is detected as the response physical quantitywaveform, and the dimension, the physical quantity of which is used asthe corresponding physical quantity waveform for control.

For example, in the case where the drive waveform is calculated at leastbased on the displacement waveform for control and the responseacceleration waveform is acquired by the sensor 6, a displacementtransfer function (a ratio of the spectrum of the response displacementwaveform to the spectrum of the drive waveform) may be calculated atleast based on the response acceleration waveform and the drivewaveform, and the reciprocal thereof may be set as the equalizationcharacteristics. The response acceleration PSD may be integrated twiceto be converted into response displacement PSD (however, it should beconsidered that the PSD is a quantity of the square of the amplitudespectrum).

As illustrated in FIG. 13 , the “displacement”, the “velocity”, the“acceleration”, and the “jerk” of the same vibration can be converted toone of the others by integration or differentiation. Accordingly, evenin the case where the dimensions of the response physical quantity,which is detected by the sensor 6, and the corresponding physicalquantity for control differ from each other, it is possible to calculatethe appropriate equalization characteristics by the conversion.

(10) In the above embodiment, the description has been made on thevibration control system for the excitation in one direction by thevibration generator 2. However, the above embodiment can be appliedsimilarly to a multi-axis vibration control system for excitation in aplurality of directions.

(11) In the above embodiment, the corresponding physical quantity PSDfor control, the dimension of which differs from that of the referencephysical quantity PSD, is generated for the control. However, thephysical quantity PSD for control, the dimension of which is the same asthat of the reference physical quantity PSD, may be generated for thecontrol. In this case, the PSD conversion means 34 is unnecessary.

(12) Each of the above modified examples can be combined with theother(s) of the modified examples or can be applied to anotherembodiment unless contrary to the nature thereof.

2. Second Embodiment

2.1 Functional Configuration

FIG. 14 is a functional block diagram of a vibration control systemaccording to another embodiment of the present invention. In thisembodiment, control is executed such that the test object 4 vibrates ina manner that the waveform thereof matches a provided referencewaveform. However, the dimension of the reference physical quantity isdifferent from that of the response quantity that is detected by thesensor 6 attached to the test object 4. That is, the dimension of thereference corresponding physical quantity waveform differs from that ofthe response physical quantity waveform.

The drive waveform calculation means 50 calculates the drive waveform atleast based on the provided reference corresponding physical quantitywaveform and by using the equalization characteristics that is thereciprocal of the transfer function of the system. This drive waveformis provided to the vibration generator 2 via the D/A converter 70 andthe amplifier 80.

The test object 4 as the test target is placed on the vibrationgenerator 2. The physical quantity detection sensor 6 detects thevibration of the test object 4 that is vibrated by the vibrationgenerator 2. A displacement sensor, a velocity sensor, an accelerationsensor, a jerk sensor, or the like can be used as the vibration physicalquantity detection sensor 6. The response vibration physical quantitysignal (the displacement signal, the velocity signal, the accelerationsignal, the jerk signal, or the like) from the vibration physicalquantity detection sensor 6 is converted into the response physicalquantity waveform as digital data by the A/D converter 10. The responsephysical quantity waveform is the data in which the characteristics ofthe vibration is expressed in the dimension such as displacement,velocity, acceleration, or jerk.

The transfer function calculation means 62 of the equalizationcharacteristics modification means 60 calculates a physical quantitytransfer function at least based on the response physical quantitywaveform and the drive waveform. That is, the transfer functioncalculation means 62 calculates the spectrum of the response physicalquantity waveform (including the phase information), calculates thespectrum of the drive waveform (including the phase information), andcalculates a ratio therebetween as the physical quantity transferfunction.

The transfer function conversion means 64 differentiates (or integrates)this physical quantity transfer function, converts the differentiated(or integrated) physical quantity transfer function to have the samedimension as the dimension of the physical quantity of the referencewaveform, and thereby acquires the corresponding physical quantitytransfer function. The inverse transfer function calculation means 66calculates the reciprocal of the corresponding physical quantitytransfer function and sets the reciprocal as the equalizationcharacteristics for the calculation of the drive waveform.

As it has been described so far, even in the case where the dimension ofthe reference waveform differs from the dimension detected by the sensor6, the control can be executed such that the test object vibrates in themanner that the waveform thereof matches the reference waveform.

2.2 Hardware Configuration

The hardware configuration is the same as that illustrated in FIG. 2 .

2.3 Vibration Control Processing

FIG. 15 illustrates a flowchart of the control program 98 (see FIG. 2 ).A description will herein be made on, as an example, a case where thephysical quantity detection sensor 6 is the velocity sensor and areference jerk waveform is provided as a reference physical quantitywaveform.

The CPU 90 takes out a single frame from the reference jerk waveform(step S51). However, the CPU 90 takes out the reference jerk waveform byshifting the reference jerk waveform by ½ frame.

The CPU 90 performs convolution operation on waveform data acquired bymultiplying the single frame of the reference jerk waveform, which istaken out by Hanning windowing, by using the impulse response as theequalization characteristics, so as to generate the drive signal (stepsS52, S53). In this embodiment, as the equalization characteristics, theinverse characteristics of the transfer function of the system includingthe vibration generator 2 and the test object 4 is used. In order tovibrate the test object 4 with the reference jerk waveform, theconvolution operation is performed on the jerk waveform for control byusing the impulse response, which corresponds to the inversecharacteristics of the transfer function, so as to generate the waveformas the drive waveform. In this way, the test object 4 can be vibrated soas to its jerk waveform matches with the reference jerk waveform.

The CPU 90 shifts the single frame of the drive signal, which isobtained by the multiplication of the window function and shifting by ½frame, by ½ frame again and superimposes the drive signal (theoverlapping processing, steps S52, S54). In this way, the CPU 90generates the continuous drive waveform and outputs this drive waveformto the amplifier 80 via the output D/A converter 70 (step S55).

As a result, the vibration generator 2 is provided with the drive signalthat is amplified by the amplifier 80, and thus can vibrate the testobject 4.

Next, the CPU 90 acquires the response velocity waveform from theacceleration sensor 6 (step S56). The CPU 90 calculates the velocitytransfer function of the system at least based on the provided drivewaveform and the corresponding response velocity waveform (step S57).That is, a response velocity signal is subjected to the FFT to calculatethe velocity spectrum (including the phase information), and the drivewaveform is subjected to the FFT to calculate the drive spectrum(including the phase information). As a ratio between the velocityspectrum and the drive spectrum, the velocity transfer function iscalculated from both of the velocity spectrum and the drive spectrum.

Next, this velocity transfer function is differentiated twice in thefrequency domain and is converted into a jerk transfer function (stepS58). That is, the velocity transfer function is converted into the jerktransfer function as a ratio between jerk spectrum and the drivespectrum. A reciprocal of the jerk transfer function, which iscalculated, is updated as the equalization characteristics (step S59).This equalization characteristics is used when the drive signal isgenerated next time.

The CPU 90 repeatedly executes the processing that has been described sofar. In this way, the test object 4 can vibrate having the propertyrequired by the provided reference jerk waveform.

2.4 Other

(1) In the above embodiment, as illustrated in FIG. 14 , theequalization characteristics modification means 60 includes the transferfunction calculation means 62, the transfer function conversion means64, and the inverse transfer function calculation means 66.

However, as illustrated in FIG. 16 , the equalization characteristicsmodification means 60 may include the conversion means 61, the transferfunction calculation means 62, and the inverse transfer functioncalculation means 66. The conversion means 61 converts the responsephysical quantity waveform into response corresponding physical quantitywaveform. The transfer function calculation means 62 calculates thecorresponding physical quantity transfer function at least based on thedrive waveform and the response corresponding physical quantitywaveform. The inverse transfer function calculation means 66 calculatesthe reciprocal of the corresponding physical quantity transfer functionas the equalization characteristics.

(2) The waveform control in the above embodiment (the control for makingthe test object vibrate just as the reference waveform itself) can beused in a control loop of the PSD control. For example, as illustratedin FIG. 17 , the waveform control can be executed in the differentdimension from the dimension of the reference physical quantity PSD.Differing from FIG. 1 , in FIG. 17 , the non-Gaussian control is notexecuted.

(3) FIG. 18 is a functional block diagram according to further anotherembodiment. In this embodiment, processing is executed to make the drivewaveform have a non-Gaussian property (by limiting the peak value or thelike).

In this embodiment, control is executed such that the test object 4vibrates in a manner that a response physical quantity PSD matches theprovided reference physical quantity PSD. The reference PSD of thedimension is the same as the dimension of the physical quantity that isdetected by the sensor 6 attached to the test object 4.

The test object 4 as the test target is placed on the vibrationgenerator 2. The vibration physical quantity detection sensor 6 detectsthe vibration of the test object that is vibrated by the vibrationgenerator 2. A displacement sensor, a velocity sensor, an accelerationsensor, a jerk sensor, or the like can be used as the vibration physicalquantity detection sensor 6. The signal representing the responsevibration physical quantity (the displacement signal, the velocitysignal, the acceleration signal, the jerk signal, or the like) from thevibration physical quantity detection sensor 6 is converted into theresponse physical quantity waveform as digital data by the A/D converter10. The response physical quantity waveform is the data in which thecharacteristics of the vibration is expressed in the dimension such asdisplacement, velocity, acceleration, or jerk.

The response physical quantity PSD calculation means 20 performs theFast Fourier Transform (FFT) on the response physical quantity waveformto calculate the response physical quantity PSD thereof. Drive PSDcontrol means 31 calculates the drive PSD at least based on the responsephysical quantity PSD, the reference physical quantity PSD, the responsephysical quantity waveform, and the drive waveform.

In this embodiment, the drive PSD control means 31 includes the means 30for calculating physical quantity PSD for control, drive PSD calculationmeans 33, and transfer characteristics calculation means 35. The means30 for calculating corresponding vibration physical quantity PSD forcontrol calculates the physical quantity PSD for control such that theresponse physical quantity PSD matches the reference physical quantityPSD. This is because, in the case where the transfer characteristic ofthe system including the vibration generator 2 and the test object 4 hasa non-linear characteristics, in the case where the control resolutionis insufficient, or due to a reason such as statistical variationsincluded in the actually-measured PSD data, the test object 4 vibratesdifferently from the vibration generated by the reference physicalquantity PSD even when the vibration having the reference physicalquantity PSD is applied to the vibration generator 2. Thus, the physicalquantity PSD for control is successively modified and calculated suchthat the response physical quantity PSD matches the reference physicalquantity PSD.

The transfer characteristics calculation means 35 calculates a transfercharacteristics H (a transfer function) of the system at least based onthe response physical quantity waveform and the drive waveform. Thedrive PSD calculation means 33 calculates the drive PSD at least basedon the physical quantity PSD for control and in consideration of thetransfer characteristics H. That is, the drive PSD is calculated bymultiplying the physical quantity PSD for control by 1/H².

Drive waveform calculation means 90 generates the non-Gaussian drivewaveform at least based on this drive PSD.

In this embodiment, the drive waveform calculation means 90 includesGaussian drive waveform calculation means 92, non-Gaussian conversionmeans 94, phase extraction means 96, and waveform calculation means 98.

The Gaussian drive waveform calculation means 92 provides the uniformrandom phase to the drive PSD, so as to calculate the Gaussian drivewaveform. The non-Gaussian conversion means 94 makes the Gaussian drivewaveform have the non-Gaussian property at least based on the prescribednon-Gaussian characteristics, so as to calculate the non-Gaussian randomwaveform. For example, the non-Gaussian conversion means 94 converts theamplitude of the drive waveform by using a ZMNL function or the like,and performs the operation (clipping) to limit the amplitude of thedrive waveform such that the amplitude (the absolute value) does notexceed a prescribed value.

The phase extraction means 96 calculates frequency characteristics ofthe phase of this non-Gaussian random waveform. The waveform calculationmeans 98 calculates the non-Gaussian drive waveform at least based onthe drive PSD and this phase information, and sets this non-Gaussiandrive waveform as the drive waveform.

Accordingly, it is possible to provide the test object 4 with thevibration that matches the reference physical quantity PSD while thedrive waveform is made to have a non-Gaussian property.

In the above description, the physical quantity PSD for control iscalculated, and the drive PSD is calculated on the basis thereof.However, the drive PSD may directly be calculated at least based on thereference physical quantity PSD, the response physical quantity PSD, andthe transfer function.

In addition, processing contents by the drive waveform calculation means90 are the same as those of the means 40 for calculating correspondingphysical quantity waveform for control. Thus, the before mentionedmodified example related to the means 40 for calculating correspondingphysical quantity waveform for control can be applied thereto.

(4) Each of the above modified examples can be combined with theother(s) of the modified examples or can be applied to anotherembodiment unless contrary to the nature thereof.

What is claimed is:
 1. A vibration control system comprising: avibration physical quantity detection sensor configured to detect avibration physical quantity of a test object that is vibrated by avibration generator operated on the basis of a drive waveform, whereinthe vibration physical quantity represents a vibration expressed as afirst dimension; a processor, memory and instructions, the instructionswhen executed: determine a response vibration physical quantity PSD(Power Spectral Density) by subjecting a response vibration physicalquantity waveform from the vibration physical quantity detection sensorto a Fourier transform; determine a corresponding vibration physicalquantity PSD for control, wherein the vibration physical quantity PSDfor control represents a vibration expressed as a second different,dimension, which corresponds to vibration physical quantity PSD forcontrol, on the basis of the response vibration physical quantity PSDand a reference vibration physical quantity PSD; determine anon-Gaussian random waveform of the corresponding vibration physicalquantity for control by subjecting spectrum data, which is generatedfrom the corresponding vibration physical quantity PSD for control, toan inverse Fourier transform in order to obtain desired non-Gaussiancharacteristics, and set the non-Gaussian random waveform of thecorresponding vibration physical quantity for control as a correspondingvibration physical quantity waveform for control; determine the drivewaveform for the vibration generator on the basis of the correspondingvibration physical quantity waveform for control with inversecharacteristics of transfer characteristics of at least the vibrationgenerator and the test object as equalization characteristics; andmodify the equalization characteristics on the basis of the drivewaveform and the response vibration physical quantity waveform, andoutputting the drive waveform, via a drive signal, to the vibrationgenerator to test the test object, wherein: the vibration physicalquantity detection sensor is configured to detect any one of adisplacement, a velocity, an acceleration, or a jerk associated with avibration of the test object, the response vibration physical quantityPSD has a selected dimension of a displacement PSD, a velocity PSD, anacceleration PSD, or a jerk PSD, and the corresponding vibrationphysical quantity PSD for control of the second, different dimension isany one of the displacement PSD, the velocity PSD, the acceleration PSDor the jerk PSD, with the second, different dimension being differentfrom the selected dimension of the response vibration physical quantityPSD.
 2. The system according to claim 1, wherein the instructions thatdetermine the corresponding vibration physical quantity PSD for controlinclude: instructions that determine a vibration physical quantity PSDfor control by comparing the response vibration physical quantity PSDand the reference vibration physical quantity PSD such that the responsevibration physical quantity PSD is equal to the reference vibrationphysical quantity PSD; and instructions that convert the vibrationphysical quantity PSD for control into the corresponding vibrationphysical quantity PSD for control of the second, different dimension. 3.The system according to claim 1, wherein the instructions that calculatethe corresponding vibration physical quantity PSD for control include:instructions that convert the response vibration physical quantity PSDinto response corresponding vibration physical quantity PSD of thesecond, different dimension; instructions that convert the referencevibration physical quantity PSD into reference corresponding vibrationphysical quantity PSD of the second, different dimension; andinstructions that modify the corresponding vibration physical quantityPSD for control by comparing the response corresponding vibrationphysical quantity PSD and the reference corresponding vibration physicalquantity PSD such that the response corresponding vibration physicalquantity PSD is equal to the reference corresponding vibration physicalquantity PSD.
 4. The system according to claim 1, wherein theinstructions that convert the corresponding vibration physical quantitywaveform for control include: instructions that acquire a Gaussianrandom waveform of the corresponding vibration physical quantity forcontrol by subjecting amplitude spectrum data, which is generated fromthe corresponding vibration physical quantity PSD for control, to theinverse Fourier transform by providing uniformly distributed randomphases; instructions that convert the Gaussian random waveform of thecorresponding vibration physical quantity for control into anon-Gaussian random waveform on the basis of non-Gaussian conversioncharacteristics; instructions that extract a phase of each frequencycomponent as a non-Gaussian signal phase by subjecting the non-Gaussianrandom waveform to the Fourier transform; and instructions thatdetermine a non-Gaussian random waveform of the corresponding vibrationphysical quantity for control by subjecting the corresponding vibrationphysical quantity PSD for control to the inverse Fourier transform byproviding the non-Gaussian signal phase.
 5. The system according toclaim 4, wherein the non-Gaussian conversion characteristic is acharacteristic that limits a peak value such that the Gaussian randomwaveform of the corresponding vibration physical quantity for controldoes not exceed a prescribed limit value, and when the Gaussian randomwaveform of the corresponding vibration physical quantity for controldoes not exceed the limit value, said Gaussian random waveform of thecorresponding vibration physical quantity for control is used as thenon-Gaussian random waveform of the corresponding vibration physicalquantity for control.
 6. The system according to claim 1, wherein theinstructions that determine the corresponding vibration physicalquantity waveform for control include: instructions that acquire aGaussian random waveform of a corresponding vibration physical quantityfor control by subjecting amplitude spectrum data, which is generatedfrom the corresponding vibration physical quantity PSD for control, tothe inverse Fourier transform by providing uniformly distributed randomphases; and instructions that convert the Gaussian random waveform ofthe corresponding vibration physical quantity for control into anon-Gaussian random waveform on the basis of non-Gaussian conversioncharacteristics such that the non-Gaussian random waveform of thecorresponding vibration physical quantity for control is obtained. 7.The system according to claim 6, wherein the non-Gaussian conversioncharacteristics is a ZMNL function.
 8. The system according to claim 1,wherein the instructions that determine the drive waveform perform aconvolution operation on the corresponding vibration physical quantitywaveform for control by using impulse response as the equalizationcharacteristics, so as to calculate the drive waveform, and theinstructions that modify the equalization characteristics calculate theequalization characteristic as a reciprocal of a value obtained bydividing the corresponding vibration physical quantity with thevibration physical quantity transfer function, on the basis of aspectrum of a response corresponding vibration physical quantitywaveform, which is converted from the response vibration physicalquantity waveform, and a spectrum of the drive waveform.
 9. The systemaccording to claim 8, wherein the instructions that modify theequalization characteristic include: instructions that determine thevibration physical quantity transfer function on the basis of the drivewaveform and the response vibration physical quantity waveform;instructions that convert the vibration physical quantity transferfunction into the corresponding vibration physical quantity transferfunction; and instructions that determine the equalizationcharacteristic as a reciprocal of the corresponding vibration physicalquantity transfer function.
 10. The system according to claim 8, whereinthe instructions that determine the drive waveform include: instructionsthat convert the corresponding vibration physical quantity waveform forcontrol into a non-Gaussian random waveform of the vibration physicalquantity for control; and instructions that perform the convolutionoperation on the physical vibration quantity waveform for control byusing the impulse response with the impulse response of the systemincluding the vibration generator and the test object as theequalization characteristics, so as to calculate the drive waveform. 11.A vibration control system comprising: an acceleration sensor configuredto detect, acceleration of a test object that is vibrated by a vibrationgenerator operated on the basis of a drive waveform; a processor andmemory, the processor executing instructions stored in memory that:acquire a response acceleration PSD by subjecting a responseacceleration waveform from the acceleration sensor to the Fouriertransform; determine a vibration physical quantity PSD for controlcorresponding to acceleration PSD for control on the basis of theresponse acceleration PSD and reference acceleration PSD, the vibrationphysical quantity PSD for control being displacement PSD for control, orvelocity PSD for control, or jerk PSD for control; determine a Gaussianrandom waveform of a corresponding vibration physical quantity forcontrol by subjecting amplitude spectrum data, which is generated fromthe displacement PSD for control, or the velocity PSD for control, orthe jerk PSD for control, to the inverse Fourier transform by providinguniformly distributed random phases, Gaussian random waveform of acorresponding vibration physical quantity for control being a Gaussianrandom waveform of displacement for control, or a Gaussian randomwaveform of velocity for control, or a Gaussian random waveform of thejerk for control; determine and provide drive waveform determinationinstructions with the Gaussian random waveform of displacement forcontrol, or the Gaussian random waveform of velocity for control, or theGaussian random waveform of jerk for control as is as a displacementwaveform for control, a velocity waveform for control, or a jerkwaveform for control in the case where any portion that exceeds a limitvalue is not present in said Gaussian random waveform of thedisplacement for control, said Gaussian random waveform of the velocityfor control, or said Gaussian random waveform of the jerk for control ina prescribed unit period, and provide the drive waveform determinationinstructions with a non-Gaussian random waveform of the displacement forcontrol, or a non-Gaussian random waveform of the velocity for control,or a non-Gaussian random waveform of the jerk for control, which isdetermined by a non-Gaussian conversion instructions, non-Gaussiansignal phase extraction instructions, and waveform calculationinstructions, as the displacement waveform for control, the velocitywaveform for control, or the jerk waveform for control in the case wherethe portion that exceeds the limit value is present; determine the drivewaveform on the basis of the displacement waveform for control, thevelocity waveform for control, or the jerk waveform for control withinverse characteristics of transfer function of a system including avibration generator and the test object as equalization characteristics;output the drive waveform, via a drive signal, to the vibrationgenerator to test the test object; determine an acceleration transferfunction on the basis of the drive waveform and the responseacceleration waveform; convert the acceleration transfer function into adisplacement transfer function, a velocity transfer function, or a jerktransfer function; and determine the equalization characteristics as areciprocal of the displacement transfer function, the velocity transferfunction, or the jerk transfer function.
 12. A vibration control systemconfigured to vibrate a test object in a manner to match a referencevibration physical quantity waveform of a second dimension that differsfrom a first dimension of a drive waveform for vibrating the test objectand of a response vibration physical quantity waveform, with whichvibration of the test body is detected, the vibration control systemcomprising: a vibration physical quantity detection sensor which detectsa vibration physical quantity of the test object that is vibrated by avibration generator operated on the basis of the drive waveform, so asto output the response vibration physical quantity waveform; aprocessor, memory and instructions, the instructions when executed:determine and output the drive waveform configured to drive thevibration generator on the basis of the reference vibration physicalquantity waveform by using equalization characteristics as inversecharacteristics of transfer characteristics of at least the vibrationgenerator and the test object; and modify the equalizationcharacteristic as a reciprocal of a second dimension transfer functionon the basis of the response vibration physical quantity waveform andthe drive waveform, the second dimension transfer function being a ratiobetween a spectrum of the drive waveform and a spectrum of a secondresponse vibration physical quantity waveform, which is acquired byconverting the response vibration physical quantity waveform into thatof the second dimension, wherein the vibration physical quantityrepresents a vibration expressed as the first dimension and wherein thereference vibration physical quantity waveform of a second dimensionrepresents a vibration expressed as a second, different dimension.